MER331   Lab 2

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Error Sources. The measurement process consists of three dis-tinct steps: calibration, data acquisition, and data reductioncalibration errordata acquisition errordata reduction error. Uncertainty Analysis. Error - difference between true value and measured value.Two general categories of error

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MER331 Lab 2

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1. MER331 – Lab 2 Uncertainty Analysis

2. Error Sources The measurement process consists of three dis-tinct steps: calibration, data acquisition, and data reduction calibration error data acquisition error data reduction error

3. Uncertainty Analysis Error - difference between true value and measured value. Two general categories of error (exclude gross blunders) Fixed error – remove by calibration Random error – quantify by uncertainty analysis The term uncertainty is used to refer to “a possible value that an error may have”

4. Stages of Uncertainty Analysis Design Stage Uncertainty Analysis Uncertainty analysis can be used to assist in the selection of equipment and procedures based on their relative performance and cost. Advanced-Stage and Single Measurement Uncertainty Analysis Consider procedural and test control errors that affect the measurement

5. Uncertainty Analysis m = Kt(rball-rfluid) How do I find uncertainty in m if I have uncertainty in K, t, rball,and rfluid.? Three steps: Estimate uncertainty interval for each measured quantity State the confidence limit on each measurement Analyze the propagation of uncertainty into results calculated from experimental data.

6. Estimating Uncertainty Interval If you have a statistically significant sample use: ±2s for a 95% confidence interval. (1st order analysis) General Practice in engineering is 95% confidence of 20 to 1 odds. Otherwise use ± ½ smallest scale division as an estimate. (0th order analysis) * Technique due to: Kline, S.J., and McClintock, F.A., “Describing Uncertainties in Single Sample Experiments,” Mechanical Engineering, 75, 1953.

7. Propagation of Uncertainty -The Basic Mathematics The value of dxi represents 2s for a single sample analysis. The result, R of an experiment is assumed to be calculated from a set of measurements: R = R(X1, X2, X3,…, XN) The effect of the uncertainty in a single measurement (i.e. one of the X’s) on the calculated result, R, if only that one X were in error is:

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